In the case where \(\sigma _{add} = \sigma _{mult} = 0\) , NFM reduces to manifold mixup [1]}. If in addition \(\mathcal {S} = \lbrace 0\rbrace \) , it reduces to the original mixup method [2]}. The main difference between NFM and manifold mixup lies in the noise injection of the fourth step above. Note that NFM is equivalent to injecting noise into \(g_k(x), g_k(x^{\prime })\)  first, then performing mixup on the resulting pair, i.e., the order that the third and fourth steps occur does not change the resulting noisy mixed minibatch. For simplicity, we have used the same mixing level, noise distribution and noise levels for all layers in \(\mathcal {S}\)  in our formulation.
